$(30$ pts$)$ Consider the model with two functional constraints and two variables given below.

and

$x_{1}0,x_{2}0.$

a$)$ Construct the dual problem for this primal problem.

b$)$ Solve both the primal$-$ and the dual$-$ problem graphically. Identify all basic solutions

$($both feasible and infeasible solutions$)$ for both problems. Calculate the objective

function values for all these solutions.

c$)$ Use the information obtained in part $($b$)$ to construct a table listing the complementary

basic solutions for these problems.